Modelling and Control of Doubly Fed Induction

Generator based stand-alone Wind Energy

Conversion System

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE

DEGREE OF

Master of Technology

In

Electrical Engineering

By

KOTA VINAY KUMAR REDDY

Roll No. 213EE4334

Department of Electrical Engineering

National Institute of Technology Rourkela

Rourkela-769008

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Modelling and Control of Doubly Fed Induction

Generator based stand-alone Wind Energy

Conversion System

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR

THE DEGREE OF

Master of Technology

In

Electrical Engineering

By

KOTA VINAY KUMAR REDDY

Under the guidance of

Prof. MONALISA PATTNAIK

Department of Electrical Engineering

National Institute of Technology Rourkela

Rourkela-769008

ii

Department of Electrical Engineering

National Institute of Technology Rourkela

Certificate

This is to certify that the thesis entitled, “Modelling and Control of Doubly Fed Induction

Generator based stand-alone Wind Energy Conversion System” submitted by Mr. Kota Vinay

Kumar Reddy in partial fulfillment of the requirements for the award of Master of Technology

Degree in Electrical Engineering with specialization in “Power Electronics and Drives” during

session 2013-15 at National Institute of Technology, Rourkela is an authentic work carried out by

him under my supervision and guidance. This work has not been submitted at other University/

Institute for the award of any degree or diploma.

Date: Prof. Monalisa Pattnaik

Place: Department of Electrical Engineering

National Institute of Technology

Rourkela-769008

iii

Acknowledgement

I would like to express my sincere gratitude to my supervisor Prof. Monalisa Pattnaik for her

guidance, encouragement, and support throughout the course of this work. It was an invaluable

learning experience for me to be one of her students. As my supervisor her insight, observations

and suggestions helped me to establish the overall direction of the research and contributed

immensely for the success of this work.

I express my gratitude to Prof. A. K. Panda, Head of the Department, Electrical

Engineering for his invaluable suggestions and constant encouragement all through this work. My

thanks are extended to my colleagues in power control and drives, who built an academic and

friendly research environment that made my study at NIT, Rourkela most fruitful and enjoyable.

I would also like to acknowledge the entire teaching and non-teaching staff of Electrical

department for establishing a working environment and for constructive discussions. Finally, I am

always indebted to all my family members, especially my parents, for their endless support and

love.

Last but not least I would like to thank my parents, who taught me to work hard by their

own example. They provided me much support being apart during the whole tenure of my stay in

NIT Rourkela.

Kota Vinay Kumar Reddy

ROLL NO. - 213EE4334

iv

Abstract

The application of wound rotor induction machine is widely spread in wind energy generating

stations because of its adaptability for variable speed wind turbines through which maximum

possible extraction of wind energy is possible. Also among all the induction generator

configurations for wind power systems the use of Doubly Fed Induction Generator (DFIG)

configuration with back to back pulse width modulated voltage source converters (VSC) is one of

the best topologies available and it is suitable for both grid connected systems as well as stand-

alone systems. Here only stand-alone application of DFIG is considered. In this thesis

mathematical modelling of doubly fed induction machine is presented. The control strategies for

both stator side converter and rotor side converter are developed in stator flux oriented reference

frame. The dynamics of dc link voltage build-up phase is also included. The stator side converter

is used to control the output voltage in direct voltage control manner and the rotor side converter

is current controlled where the power imbalance of the system is nullified using dc link voltage

controller which modifies the quadrature axis rotor current reference value according to the

changes in the wind speed as well as the load. Two control algorithms are presented out of which

one gives the best performance for all kinds of loads (balance, unbalance, linear and non-linear)

and the other gives poor load regulation and unwanted distortions in the output voltage for non-

linear and unbalanced loads.

v

Table of Contents

Certificate ........................................................................................................................................ ii

Acknowledgement ......................................................................................................................... iii

Abstract .......................................................................................................................................... iv

List of figures ................................................................................................................................ vii

List of Abbreviations ..................................................................................................................... ix

CHAPTER 1 ................................................................................................................................... 1

INTRODUCTION .......................................................................................................................... 1

1.1 IMPORTANCE OF DFIG IN WECS .............................................................................. 2

1.2 LITERATURE SURVEY ................................................................................................ 3

1.3 MOTIVATION ................................................................................................................ 5

1.4 OBJECTIVES .................................................................................................................. 6

1.5 THESIS ORGANISATION ............................................................................................. 6

CHAPTER 2 ................................................................................................................................... 8

MATHEMATICAL MODEL OF DFIG ........................................................................................ 8

2.1 INTRODUCTION ............................................................................................................ 8

2.2 DFIG MODELS ............................................................................................................... 9

2.2.1 MODEL OF DFIG IN ABC REFERENCE FRAME ............................................. 10

2.2.2 MODEL OF DFIG IN STATIONARY REFERENCE FRAME ........................... 14

2.2.4 MODEL OF DFIG IN SYNCHRONOUS REFERENCE FRAME ....................... 16

CHAPTER 3 ................................................................................................................................. 19

OPEN LOOP CONTROL STRATEGY FOR DFIG BASED STAND-ALONE WECS ............ 19

3.1 INTRODUCTION .......................................................................................................... 19

3.2 DYNAMIC MODEL OF INDUCTION MACHINE..................................................... 20

3.3 STATOR SIDE CONVERTER CONTROL ................................................................. 22

vi

3.4 SPWM TECHNIQUE .................................................................................................... 24

3.5 ROTOR SIDE CONVERTER CONTROL.................................................................... 25

3.6 SIMULATION RESUTLS AND DISCUSSION .......................................................... 27

CHAPTER 4 ................................................................................................................................. 33

CLOSED LOOP CONTROL STRATEGY FOR DFIG BASED STAND-ALONE WECS ....... 33

4.1 INTRODUCTION .......................................................................................................... 33

4.2 STATOR SIDE CONVERTER CONTROL ................................................................. 35

4.3 SIMULATION RESULTS AND DISCUSSION .......................................................... 37

CHAPTER 5 ................................................................................................................................. 42

CONCLUSIONS AND FUTURE SCOPE ................................................................................... 42

REFERENCES ............................................................................................................................. 44

vii

List of figures

Fig. 1.1 Components of WECS scheme.......................................................................................... 1

Fig. 2.1 Schematic of DFIG based WECS ...................................................................................... 9

Fig. 2.2 Cross sectional view of WRIM ....................................................................................... 10

Fig. 2.3 Schematic of axes transformation (ABC to αβ). ............................................................. 14

Fig. 2.4 Schematic of axes transformation (ABC to dq). .............................................................. 16

Fig. 2.5(a) q-axis equivalent circuit of WRIM in synchronous frame. ......................................... 18

Fig. 2.5(b) d-axis equivalent circuit of WRIM in synchronous frame.......................................... 18

Fig. 3.1 Schematic of DFIG based WECS with open loop control strategy ................................. 19

Fig. 3.2 Block diagram of stator converter control scheme .......................................................... 22

Fig. 3.3 Modulation signal for SPWM technique ......................................................................... 24

Fig. 3.4 Block diagram of rotor converter control scheme ........................................................... 26

Fig. 3.5(a) unit vector sine(θs) ...................................................................................................... 27

Fig. 3.5(b) unit vector cos(θs) ....................................................................................................... 27

Fig. 3.6 Rotor speed ...................................................................................................................... 28

Fig. 3.7 Rotor current in synchronous reference frame ................................................................ 28

Fig. 3.8 dc link voltage profile ...................................................................................................... 29

Fig. 3.9 Load current ..................................................................................................................... 29

Fig. 3.10 Load voltage profile....................................................................................................... 29

Fig. 3.11 FFT analysis of load voltage ........................................................................................ 29

Fig. 3.12 Stator flux ...................................................................................................................... 30

Fig. 3.13 Stator voltage in synchronous reference frame ............................................................. 30

Fig. 3.14 Stator current profile ...................................................................................................... 30

viii

Fig. 3.15 FFT analysis of stator current ........................................................................................ 30

Fig. 3.16 Load voltage profile for nonlinear load (open loop control) ......................................... 31

Fig. 3.17 Load current profile for nonlinear load transient ........................................................... 31

Fig. 3.18 FFT analysis of load voltage for nonlinear load (open loop control) ............................ 31

Fig. 4.1 Schematic of DFIG based stand-alone system with closed loop control scheme ........... 34

Fig. 4.2 d-axis equivalent circuit. .................................................................................................. 35

Fig. 4.3 q-axis equivalent circuit ................................................................................................... 35

Fig. 4.4 Block diagram of stator voltage controller. ..................................................................... 37

Fig. 4.5 dc link voltage profile ...................................................................................................... 38

Fig. 4.6 Rotor current in synchronous reference frame ................................................................ 38

Fig. 4.7 Stator flux ........................................................................................................................ 38

Fig. 4.8 Stator voltage in synchronous reference frame ............................................................... 39

Fig. 4.9 Stator current ................................................................................................................... 39

Fig. 4.10 Load current ................................................................................................................... 39

Fig. 4.11 Load voltage .................................................................................................................. 39

Fig. 4.12 Load current for nonlinear load ..................................................................................... 40

Fig. 4.13 Stator current for nonlinear load .................................................................................... 40

Fig. 4.14 FFT analysis of stator current ........................................................................................ 40

Fig. 4.15 Load voltage for nonlinear load (closed loop control) .................................................. 40

Fig. 4.16 FFT analysis of load voltage for nonlinear load (closed loop control) ......................... 41

ix

List of Abbreviations

DFIG Doubly-Fed Induction Generator

IGBT Insulated Gate Bipolar Transistor

PMSG Permanent Magnet Synchronous Generator

PWM Pulse Width Modulation

PI Proportional and Integral

SPWM Sinusoidal Pulse Width Modulation

SVPWM Space Vector Pulse Width Modulation

VSC Voltage Source Converter

VSCF Variable Speed Constant Frequency

VSI Voltage Source Inverter

WECS Wind Energy Conversion Systems

WTGS Wind Turbine Generating Systems

WRIM Wound Rotor Induction Machine

1

CHAPTER 1

INTRODUCTION

As the availability of conventional energy resources is going down day by day there is a serious

need for use of alternate renewable sources such as solar cells, wind turbines, hydro power and

biomass etc. There are many engineers and several institutes responsible for making optimal

utilization of all these non-conventional energy sources possible.

Out of all the above mentioned sources wind power has its own importance because of the various

advancements and improved performance of several Wind Energy Conversion Systems (WECS).

Most of the global energy is being increasingly generated by modern wind power systems.

Germany is among the biggest wind power markets. Along with Germany there are many countries

like US, Spain, France, Denmark, China and India as well which considers wind energy as a serious

alternate for generation of electricity. Because of this a major focus is kept on wind power

conversion systems in the current thesis.

Fig. 1.1 Components of WECS scheme.

2

Different stages of a wind power generating system consisting of electro mechanical energy

conversion devices, electrical components, mechanical components and aerodynamic components

is shown in Fig. 1.1.

1.1 IMPORTANCE OF DFIG IN WECS

All the wind turbines used can be majorly categorized in to the following two types. Fixed speed

wind turbines and variable speed wind turbines. In fixed speed wind turbines the electromechanical

energy conversion device used can be of synchronous machine type where there will be a

mechanical speed control through gear ratio in between the wind turbine and the machine shaft.

This leads to increased mechanical losses which in turn reduces the efficiency of the overall energy

conversion process. On the other hand a partial variable speed wind turbine uses asynchronous

machine for mechanical energy to electrical energy conversion which can automatically vary its

rotor slip for variations in wind speed. Also a Doubly Fed Induction Generator (DFIG) with ac-

dc-ac converter in between stator and rotor windings is adaptable for variable speed wind turbines

without any gear ratio control. This topology has distinct advantages where the speed range can

be extended on both sides of synchronous speed depending on the voltage rating of the rotor. Also

as the power electronic converter used here is of lower rating as it has to deal only with the slip

power, the converter losses will be low and the cost will also become less. There are some more

advantages like the harmonic injection will be low if it is grid connected operation. On the other

hand a Permanent Magnet Synchronous Generator (PMSG) can be used with a power electronic

converter rated at the machine level. In this topology the output terminals are connected to the

power grid via a power converter which is rated at the generator power level. Sometimes a direct

driven multipole machine is considered for gearless operation.

3

All in all a wind turbine with varying speed is considered more effective compared to that of a

wind turbine which rotates at a particular fixed speed because of several disadvantages of fixed

speed turbines like high mechanical stress during wind gusts and so on. In the current thesis more

emphasis is thrown only on DFIG based variable speed Wind Turbine Generating Systems

(WTGS). Also there are several advantages of DFIG based systems compared to PMSG generating

systems some of which are listed as follows.

1. Construction of DFIG is robust and is comparatively less costly than PMSG.

2. Power can be generated from stator as well as rotor which results in higher output power.

3. In DFIG based WTGS the power converter is typically rated around thirty percent of the

rated power which makes the entire system to be cost effective and gives an overall

improved performance.

Even though the DFIG system needs regular maintenance and has complex control structures

compared to PMSG, they are widely used in wind turbine industry for large rated systems. Hence

only DFIG systems will be focused here along with the mathematical modelling and control

structures for DFIG based stand-alone WECS system. The major reason behind consideration of

stand-alone system is that in some remote parts of the world it is very difficult to maintain electrical

supply through power grid because of economical and operational difficulties. Therefore in those

areas wind energy based stand-alone systems can be used to supply regional loads based on their

geographical location. Hence DFIG systems operating in stand-alone mode are emphasized.

1.2 LITERATURE SURVEY

This section gives a brief review of various literatures available on DFIG based wind turbine

generating systems. To be more precise it consist of study carried out by many researchers on

4

modelling, control schemes and different power electronic converter topologies used in DFIG

based WTGS.

DFIG modelling

In wind turbine generator systems the standard type DFIG and brushless type DFIG are

mostly used. In reference [1] brushless DFIG employed with two cascaded induction

machines is developed and a closed loop control scheme designed in stator flux orientation

is used for commanding the active power along with the reactive power. In [2] and [3]

authors considered synchronously rotating reference frame for design of control strategies

because of its capability of reducing the complexity by converting the alternating quantities

in to dc quantities. In [3] the author considered a third order model consisting of direct

current components of stator currents and compared with a full order model under different

wind speed situations. In [4] the author proposed a new third order model without

considering resistance and inductance of stator winding and compared with a full order

model for transient performance. Due to similarity between Squirrel Cage Induction

Generator (SCIG) and DFIG the difference being that the rotor winding terminals are

available for external connection in case of DFIG the simplified models of squirrel cage

induction generator can sometimes come in handy for understanding the modelling of

DFIG and interested readers can find them in [5] and [6].

Power converter modelling

A back to back PWM converter topology is mostly used in DFIG based WTGS irrespective

to the mode of operation of the system. In [7] the author deduced the mathematical model

expressed in ABC reference frame based on space vectors. The elaborative work regarding

5

modelling of PWM converter along with changing the axis from ABC to dqO is shown in

[8]-[10].

Control strategy for DFIG based stand-alone WECS

There are several literatures available regarding DFIG based wind energy systems. The

operation of grid connected DFIG systems is more extensively presented in the initial

stages of research on DFIG based wind energy systems. The authors explained grid

connected DFIG based WECS with different control structures in references [11]-[13].

Less attention is paid for stand-alone DFIG based systems in the initial stages but R. Pena

et.al [14] proposed the design of such systems where stator flux is forced to align with a

reference frame which is predefined and also rotates at constant angular frequency. The

major issue here is that during sudden disturbances at the stator terminals the field

orientation is not properly achieved resulting in unwanted transients in the output voltage.

Speed sensor less control strategy using direct control method is proposed in [15]-[16]. The

control strategy proposed is load dependent and transient results are shown for only

resistive load. In [17] the authors proposed a new control algorithm where the voltage at

the output terminals is governed by open loop scheme and also included the analysis of rise

of voltage at the dc link capacitor terminals. A new control strategy for maintaining

constant magnitude and fixed frequency voltage profile regardless to the sudden changes

in load along with the speed variation is proposed in [18] and the evaluation for different

load categories is also included in reference [18].

1.3 MOTIVATION

In some remote places it is difficult to maintain power supply through grid because of economical

and operation difficulties. In such places depending on their geographical location and availability

6

of wind energy DFIG based stand-alone wind energy conversion systems can be adopted to supply

the regional loads. Also this topology results in higher output power if the speed is above

synchronous speed.

The power converters that are used in DFIG based systems are required to handle only part of the

overall machine power rating which leads to several advantages like lower converter losses and

also results in an overall cost effective system. Also DFIG based stand-alone WECS can be

designed with a capability of feeding all types of loads.

1.4 OBJECTIVES

The following includes the major objectives of this project work.

To maintain constant magnitude and constant frequency voltage profile at the generator

terminals irrespective of load variation and changes in prime mover speed.

To achieve improved transient performance of the entire system during load transients and

changes in prime mover speed.

To get satisfactory operation of the developed model for different load categories which

might include an unbalanced nonlinear load as well.

1.5 THESIS ORGANISATION

This entire thesis consists of five chapters along with this current introductory chapter. In the

second chapter mathematical modelling of DFIG is presented which includes the dynamic models

of induction machine in several reference frames along with active power, reactive power and

torque calculation. In the third chapter a control algorithm for DFIG based WECS in stand-alone

mode is presented which majorly concerns the output voltage and frequency control. It controls

7

the output voltage in direct voltage control manner in open loop mode i.e. without any feedback

from output side. This control strategy is tested for linear and nonlinear loads where it gives poor

load voltage regulation and unwanted distortions in the load voltage profile for nonlinear loads. In

the fourth chapter a different control algorithm is presented which controls the output voltage in

closed loop manner which include stator voltage controllers. This model is tested for all kinds of

loads and it gives satisfactory results for nonlinear loads as well without any distortions in the load

voltage. In the last chapter i.e. in fifth chapter conclusions and scope for further studies are

presented.

8

CHAPTER 2

MATHEMATICAL MODEL OF DFIG

In wind energy generation systems the power extraction and conversion process is majorly done

in two steps. In first step the kinetic energy possessed by wind is converted in to mechanical energy

using aero-dynamics and turbines. The second step is carried out by electrical generator which is

DFIG in the present system. In order to examine the various issues associated with stand-alone

WECS, a proper model of the system should be established first.

In this chapter wind energy conversion system is introduced first and then a complete focus is

given for DFIG model expressed in stationary ABC reference frame and dynamic models of DFIG

in rotating reference frames are established using the classical transformations.

2.1 INTRODUCTION

The schematic of stand-alone variable speed WECS is shown in Fig. 2.1. The stator winding

terminals are connected to the load via a filter and back to back VSC converters are connected

between stator and rotor terminals which is clear from the schematic diagram in Fig. 2.1. These

converters are bidirectional converters made of Insulated Gate Bipolar Transistor (IGBT) switches

with anti-back diodes connected in parallel across each switch which makes the flow of

bidirectional current possible. The control system that governs the stator and rotor converters are

designed to achieve the desired objectives and to control the dynamic performance of the system.

9

Fig. 2.1 Schematic of DFIG based WECS

The two converters are named as stator converter and rotor converter with a capacitor connected

in between them as described in Fig. 2.1. The converter in the load side is controlled to get the

desired output voltage profile and the converter in the machine side is controlled to maintain power

balance of the system by governing the voltage at dc link capacitor.

2.2 DFIG MODELS

Design of vector control principles demands better understanding of the machine transient

behavior which can be done using the study of dynamic models of the machine. The mathematical

representation of machine that is necessary for control structure design should include all the

dynamic effects that comes in to picture while the model is in steady state and transient mode [19].

Such a model which is effective for all the arbitrary and instantaneous variations in both voltages

and currents and also that describes the machine under transients along with steady state is

presented in this current section.

10

2.2.1 MODEL OF DFIG IN ABC REFERENCE FRAME

A simple two pole three phase slip ring induction machine is considered for mathematical

modelling. The schematic of the machine in its cross sectional view is shown in Fig. 2.2.

Fig. 2.2 Cross sectional view of WRIM

The machine is characterized by the following assumptions as mentioned below [19]:

1 Air gap is uniform.

2 Saturation effect is neglected.

3 Three phase windings are uniformly distributed so that per phase resistance and inductance is

same for all the three phases.

4 The distribution of flux is sinusoidal along the air gap periphery.

5 Core losses are neglected and only resistive drops are considered.

11

Each phase is considered by means of a single coil due to the resemblance of all the three phases.

That is each phase winding of the machine is represented with the help of a single coil as shown

in Fig. 2.2. The subscripts ‘A, B and C’ are used to represent stator quantities and ‘a, b and c’

represent rotor quantities. The coils representing stator windings are A, B and C and their

corresponding voltages are presented as follows:

𝑣𝐴 = 𝑟𝐴𝑖𝐴 +𝑑

𝑑𝑡(𝜓𝐴) (2.1)

Where

𝜓𝐴 = (𝐿𝐴𝐴𝑖𝐴 + 𝐿𝐴𝐵𝑖𝐵 + 𝐿𝐴𝐶𝑖𝐶 + 𝐿𝐴𝑎𝑖𝑎 + 𝐿𝐴𝑏𝑖𝑏 + 𝐿𝐴𝑐𝑖𝑐) (2.2)

i.e.

𝑣𝐴 = 𝑟𝐴𝑖𝐴 +𝑑

𝑑𝑡(𝐿𝐴𝐴𝑖𝐴 + 𝐿𝐴𝐵𝑖𝐵 + 𝐿𝐴𝐶𝑖𝐶 + 𝐿𝐴𝑎𝑖𝑎 + 𝐿𝐴𝑏𝑖𝑏 + 𝐿𝐴𝑐𝑖𝑐) (2.3)

Similarly the expressions for the other two stator voltages are written below

𝑣𝐵 = 𝑟𝐵𝑖𝐵 +𝑑

𝑑𝑡(𝐿𝐵𝐴𝑖𝐴 + 𝐿𝐵𝐵𝑖𝐵 + 𝐿𝐵𝐶𝑖𝐶 + 𝐿𝐵𝑎𝑖𝑎 + 𝐿𝐵𝑏𝑖𝑏 + 𝐿𝐵𝑐𝑖𝑐) (2.4)

𝑣𝐶 = 𝑟𝐶𝑖𝐶 +𝑑

𝑑𝑡(𝐿𝐶𝐴𝑖𝐴 + 𝐿𝐶𝐵𝑖𝐵 + 𝐿𝐶𝐶𝑖𝐶 + 𝐿𝐶𝑎𝑖𝑎 + 𝐿𝐶𝑏𝑖𝑏 + 𝐿𝐶𝑐𝑖𝑐) (2.5)

𝑟𝐴 = 𝑟𝐵 = 𝑟𝐶 = 𝑟𝑆 (2.6)

The coils representing rotor windings are a, b, and c and their corresponding voltage equations are

given below

𝑣𝑎 = 𝑟𝑎𝑖𝑎 +𝑑

𝑑𝑡(𝐿𝑎𝑎𝑖𝑎 + 𝐿𝑎𝑏𝑖𝑏 + 𝐿𝑎𝑐𝑖𝑐 + 𝐿𝐴𝑎𝑖𝐴 + 𝐿𝐵𝑎𝑖𝐵 + 𝐿𝐶𝑎𝑖𝐶) (2.7)

𝑣𝑏 = 𝑟𝑏𝑖𝑏 +𝑑

𝑑𝑡(𝐿𝑏𝑎𝑖𝑎 + 𝐿𝑏𝑏𝑖𝑏 + 𝐿𝑏𝑐𝑖𝑐 + 𝐿𝐴𝑏𝑖𝐴 + 𝐿𝐵𝑏𝑖𝐵 + 𝐿𝐶𝑏𝑖𝐶) (2.8)

12

𝑣𝑐 = 𝑟𝑐𝑖𝑐 +𝑑

𝑑𝑡(𝐿𝑐𝑎𝑖𝑎 + 𝐿𝑐𝑏𝑖𝑏 + 𝐿𝑐𝑐𝑖𝑐 + 𝐿𝐴𝑐𝑖𝐴 + 𝐿𝐵𝑐𝑖𝐵 + 𝐿𝐶𝑐𝑖𝐶) (2.9)

The resistance of each phase winding of the rotor is assumed to be equal and let it be denoted by

′𝑟𝑟′.

𝐿𝐴𝐴 = 𝐿𝐵𝐵 = 𝐿𝐶𝐶 = 𝐿𝑆𝑆 (2.10)

𝐿𝐴𝐵 = 𝐿𝐵𝐶 = 𝐿𝐶𝐴 = 𝐿𝑆𝑀 (2.11)

𝐿𝑎𝑎 = 𝐿𝑏𝑏 = 𝐿𝑐𝑐 = 𝐿𝑟𝑟 (2.12)

𝐿𝑎𝑏 = 𝐿𝑏𝑐 = 𝐿𝑐𝑎 = 𝐿𝑟𝑚 (2.13)

All the above inductive coefficients are not time variant as the displacement between the

corresponding windings is always fixed irrespective of the rotor winding position. Now coming to

the mutual inductance terms between stator and rotor windings, they are time variant as the rotor

winding is changing its angular position with respect to time. The expressions for these coefficients

are functions of the angular position of the rotor which are given below

𝐿𝐴𝑎 = 𝐿𝐵𝑏 = 𝐿𝐶𝑐 = 𝐿𝑟𝑠𝑚 cos(𝜎) (2.14)

𝐿𝐴𝑏 = 𝐿𝐵𝑐 = 𝐿𝐶𝑎 = 𝐿𝑟𝑠𝑚 cos(𝜎 + 2𝜋3⁄ ) (2.15)

𝐿𝐴𝑐 = 𝐿𝐵𝑎 = 𝐿𝐶𝑏 = 𝐿𝑟𝑠𝑚 cos(𝜎 − 2𝜋3⁄ ) (2.16)

Where 𝐿𝑟𝑠𝑚 indicates the inductance that is mutual for stator and rotor windings which is

maximum and 𝜎 is the angle shown in Fig. 2.2. The mathematical model describing a WRIM in

ABC reference frame is shown in matrix form in equation (2.17).

13

[ 𝑉𝐴

𝑉𝐵

𝑉𝐶

⋯𝑉𝑎

𝑉𝑏

𝑉𝑐 ]

=

[ 𝑟𝑠00…000

0𝑟𝑠0…000

00𝑟𝑠…000

⋮⋮⋮⋮⋮⋮⋮

000…𝑟𝑟00

000…0𝑟𝑟0

000…00𝑟𝑟]

[ 𝐼𝐴𝐼𝐵𝐼𝐶⋯𝐼𝑎𝐼𝑏𝐼𝑐 ]

+ 𝑑

𝑑𝑡

[

𝐿𝑠𝑠

𝐿𝑠𝑚

𝐿𝑠𝑚

……𝐿𝑟𝑠𝑚 cos(𝜎)

𝐿𝑟𝑠𝑚 cos(𝜎 + 2𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎 + 4𝜋3⁄ )

𝐿𝑠𝑚

𝐿𝑠𝑠

𝐿𝑠𝑚

……

𝐿𝑟𝑠𝑚 cos(𝜎 + 4𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎)

𝐿𝑟𝑠𝑚 cos(𝜎 + 2𝜋3⁄ )

𝐿𝑠𝑚

𝐿𝑠𝑚

𝐿𝑠𝑠

……

𝐿𝑟𝑠𝑚 cos(𝜎 + 2𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎 + 4𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎)

⋮⋮⋮⋮⋮⋮⋮

.

⋮⋮ ⋮⋮⋮⋮⋮

𝐿𝑟𝑠𝑚 cos(𝜎)

𝐿𝑟𝑠𝑚 cos(𝜎 + 4𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎 + 2𝜋3⁄ )

……𝐿𝑟𝑟

𝐿𝑟𝑚

𝐿𝑟𝑚

𝐿𝑟𝑠𝑚 cos(𝜎 + 2𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎)

𝐿𝑟𝑠𝑚 cos(𝜎 + 4𝜋3⁄ )

……𝐿𝑟𝑚

𝐿𝑟𝑟

𝐿𝑟𝑚

𝐿𝑟𝑠𝑚 cos(𝜎 + 4𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎 + 2𝜋3⁄ )

𝐿𝑟𝑠𝑚 cos(𝜎)……𝐿𝑟𝑚

𝐿𝑟𝑚

𝐿𝑟𝑟 ]

[ 𝐼𝐴𝐼𝐵𝐼𝐶⋯𝐼𝑎𝐼𝑏𝐼𝑐 ]

(2.17)

Form the above matrix form it is clear that inductance matrix is time variant which depends on

position of the rotor. So in order to reduce the complexity involved with time varying quantities

dqo reference frames are preferred to model induction machine which transforms the time varying

quantities in to constant quantities and thus results in constant voltages and currents along with

constant inductive coefficients.

14

2.2.2 MODEL OF DFIG IN STATIONARY REFERENCE FRAME

As seen in the above section where DFIG model is expressed in ABC reference frame the

coefficients of mutual inductance terms are varying in nature which makes it difficult for the

analysis of the machine. Hence classical transformations came in to picture which makes these

coefficients to remain constant by making all the rotor and stator windings to remain at a constant

angular displacement at all times. This is possible by converting the rotor and stator windings in

to two phase equivalent virtual windings which are stationary to each other. Using this

transformation concept the dynamic model of WRIM is developed in a synchronously rotating

reference frame and stationary reference frame as well. In the current section dynamic model of

induction machine in stationary reference frame is presented.

Fig. 2.3 Schematic of axis transformation (ABC to αβ).

Consider the diagram shown in Fig. 2.3 where the stationary α-axis is assumed to be aligned with

the magnetic axis of stator phase A winding. Now let us assume that the stator and rotor variables

15

are transformed in to α-β axes which are stationary as shown in Fig. 2.3. The corresponding

transformation matrices can easily be derived as follows. Let 𝑀𝑠𝑠𝑡 and 𝑀𝑟𝑠𝑡 indicate the matrices

for transforming stator and rotor quantities respectively which are given as follows [20]:

𝑀𝑠𝑠𝑡 =2

3

[ 1 −1

2⁄ −12⁄

0 √32

⁄ −√32

⁄

12⁄

12⁄

12⁄ ]

(2.18)

𝑀𝑟𝑠𝑡 =2

3

[ cos(𝜎)

sin(𝜎)1

2⁄

cos(𝜎 + 2𝜋3⁄ )

sin(𝜎 + 2𝜋3⁄ )

12⁄

cos(𝜎 + 4𝜋3⁄ )

sin(𝜎 + 4𝜋3⁄ )

12⁄ ]

(2.19)

The final voltage and flux linkage equations that represent the dynamic model of induction

machine in stationary reference frame (α-β) are given below (2.20)-(2.27).

𝑣𝛼𝑠 = 𝑟𝑠𝑖𝛼𝑠 +𝑑

𝑑𝑡𝜓𝛼𝑠 (2.20)

𝑣𝛽𝑠 = 𝑟𝑠𝑖𝛽𝑠 +𝑑

𝑑𝑡𝜓𝛽𝑠 (2.21)

𝑣𝛼𝑟 = 𝑟𝑟𝑖𝛼𝑟 +𝑑

𝑑𝑡𝜓𝛼𝑟 + 𝜔𝑟𝜓𝛽𝑟 (2.22)

𝑣𝛽𝑟 = 𝑟𝑟𝑖𝛽𝑟 +𝑑

𝑑𝑡𝜓𝛽𝑟 − 𝜔𝑟𝜓𝛼𝑟 (2.23)

𝜓𝛼𝑠 = 𝐿𝑠𝑖𝛼𝑠 + 𝐿𝑚𝑖𝛼𝑟 (2.24)

𝜓𝛽𝑠 = 𝐿𝑠𝑖𝛽𝑠 + 𝐿𝑚𝑖𝛽𝑟 (2.25)

𝜓𝛼𝑟 = 𝐿𝑟𝑖𝛼𝑟 + 𝐿𝑚𝑖𝛼𝑠 (2.26)

𝜓𝛽𝑟 = 𝐿𝑟𝑖𝛽𝑟 + 𝐿𝑚𝑖𝛽𝑠 (2.27)

16

2.2.3 MODEL OF DFIG IN SYNCHRONOUS REFERENCE FRAME

The model of WRIM expressed in d-q reference frame rotating at synchronous speed is derived by

considering the axis position as shown in Fig. 2.4. Synchronously rotating d-axis is shown at an

angle of 𝜎𝑠 ahead of stator phase A winding axis and rotor phase a coil axis is 𝜎 ahead of stator

phase A coil axis. Let 𝜔𝑠 be the synchronous speed with which d-q axes rotate.

Fig. 2.4 Schematic of axis transformation (ABC to dq).

As explained in the previous cases the transformation matrices for transforming the stator and rotor

variables are derived by projecting them on to d-q axes considering the schematic in Fig. 2.4. Let

𝑀𝑠 and 𝑀𝑟 be the transformation matrices for stator and rotor quantities respectively. These

matrices are given in the following equations (2.28)-(2.29).

17

𝑀𝑠 =2

3

[ cos(𝜎𝑠)

−sin(𝜎𝑠)1

2⁄

cos(𝜎𝑠 − 2𝜋3⁄ )

−sin(𝜎𝑠 − 2𝜋3⁄ )

12⁄

cos(𝜎𝑠 − 4𝜋3⁄ )

−sin(𝜎𝑠 − 4𝜋3⁄ )

12⁄ ]

(2.28)

𝑀𝑟 =2

3

[ cos(𝜎𝑠 − 𝜎)

−sin(𝜎𝑠 − 𝜎)1

2⁄

cos ((𝜎𝑠 − 𝜎) − 2𝜋3⁄ )

−sin ((𝜎𝑠 − 𝜎) − 2𝜋3⁄ )

12⁄

cos ((𝜎𝑠 − 𝜎) − 4𝜋3⁄ )

−sin ((𝜎𝑠 − 𝜎) − 4𝜋3⁄ )

12⁄ ]

(2.29)

The voltage and flux linkage equations are given as follows (2.30)-(2.37). Here the subscript ‘s’

denotes stator quantity and ‘r’ represents rotor quantity and all the rotor quantities are referred to

the stator.

𝑣𝑑𝑠 = 𝑟𝑠𝑖𝑑𝑠 +𝑑

𝑑𝑡𝜓𝑑𝑠 − 𝜔𝑠𝜓𝑞𝑠 (2.30)

𝑣𝑞𝑠 = 𝑟𝑠𝑖𝑞𝑠 +𝑑

𝑑𝑡𝜓𝑞𝑠 + 𝜔𝑠𝜓𝑑𝑠 (2.31)

𝑣𝑑𝑟 = 𝑟𝑟𝑖𝑑𝑟 +𝑑

𝑑𝑡𝜓𝑑𝑟 − (𝜔𝑠 − 𝜔𝑟)𝜓𝑞𝑟 (2.32)

𝑣𝑞𝑟 = 𝑟𝑟𝑖𝑞𝑟 +𝑑

𝑑𝑡𝜓𝑞𝑟 + (𝜔𝑠 − 𝜔𝑟)𝜓𝑑𝑟 (2.33)

𝜓𝑑𝑠 = 𝐿𝑠𝑖𝑑𝑠 + 𝐿𝑚𝑖𝑑𝑟 (2.34)

𝜓𝑞𝑠 = 𝐿𝑠𝑖𝑞𝑠 + 𝐿𝑚𝑖𝑞𝑟 (2.35)

𝜓𝑑𝑟 = 𝐿𝑟𝑖𝑑𝑟 + 𝐿𝑚𝑖𝑑𝑠 (2.36)

𝜓𝑞𝑟 = 𝐿𝑟𝑖𝑞𝑟 + 𝐿𝑚𝑖𝑞𝑠 (2.37)

18

The equivalent circuit representation of dynamic model of induction machine in synchronous

reference frame is shown in Fig. 2.5.

Fig. 2.5(a) q-axis equivalent circuit of WRIM

Fig. 2.5(b) d-axis equivalent circuit of WRIM

In general the expressions for torque, active power and reactive power in dq synchronous reference

frame are given in equations (2.38)-(2.40) as follows.

𝑇𝑒 = 𝜓𝑑𝑟𝑖𝑞𝑟 − 𝜓𝑞𝑟𝑖𝑑𝑟 (2.38)

𝑃𝑠 =3

2(𝑉𝑞𝑠𝐼𝑞𝑠 + 𝑉𝑑𝑠𝐼𝑑𝑠) (2.39)

𝑄𝑠 =3

2(𝑉𝑞𝑠𝐼𝑑𝑠 − 𝑉𝑑𝑠𝐼𝑞𝑠) (2.40)

19

CHAPTER 3

OPEN LOOP CONTROL STRATEGY FOR DFIG BASED

STAND-ALONE WECS

3.1 INTRODUCTION

The model of DFIG based stand-alone WECS with open loop control structure is shown in Fig.

3.1. There is a WRIM with two back to back VSC converters coupled with a common dc link

capacitor. The two converters are named as stator side converter and rotor side converter. The

stator converter terminals are connected to the stator terminals directly without any filter in

between them. The rotor side converter is connected to the rotor terminals and the rotor shaft of

the induction machine is driven by a prime mover as shown in Fig. 3.1. The load is connected at

the capacitor filter junction which is in turn connected to the stator terminals via an inductive filter

as shown in Fig. 3.1. Because of this inductive filter in between the load and stator terminals the

model is expected to give poor load voltage regulation. Here the model works in two modes i.e.

buildup of voltage at dc link capacitor and constant frequency generation mode.

Fig. 3.1 Schematic of DFIG based WECS with open loop control strategy

20

Once as the voltage at the dc link capacitor terminals reaches up to the desired reference value

thereafter the load should be connected for constant voltage and frequency maintenance. For

achieving this, the load is connected at the filter capacitor junction via a three phase circuit breaker

as shown in Fig. 3.1.

For this model the output voltage control is achieved in a direct voltage control manner which is

implemented using the stator side converter where the reference voltage signals are generated in

dq reference frame. The rotor converter is current controlled where the q-axis rotor current is used

to control the power imbalance of the system and the direct axis component is left undisturbed

after the dc link voltage reaches to its desired value. Both stator and rotor side converter controllers

are modeled in dq reference frame which is forced to align with the stator flux linkage space vector.

Hence the dynamic model of the WRIM in stator flux oriented reference frame is considered for

modelling the system. The equations that describe the dynamic model in stator flux reference frame

are deduced as follows.

3.2 DYNAMIC MODEL OF INDUCTION MACHINE

The general voltage and flux linkage equations of slip ring induction machine in dq reference

frame which rotates with a speed of 𝜔𝑠 rad/sec are given below.

𝑣𝑑𝑠 = 𝑟𝑠𝑖𝑑𝑠 +𝑑

𝑑𝑡𝜓𝑑𝑠 − 𝜔𝑠𝜓𝑞𝑠 (3.1)

𝑣𝑞𝑠 = 𝑟𝑠𝑖𝑞𝑠 +𝑑

𝑑𝑡𝜓𝑞𝑠 + 𝜔𝑠𝜓𝑑𝑠 (3.2)

𝑣𝑑𝑟 = 𝑟𝑟𝑖𝑑𝑟 +𝑑

𝑑𝑡𝜓𝑑𝑟 − (𝜔𝑠 − 𝜔𝑟)𝜓𝑞𝑟 (3.3)

𝑣𝑞𝑟 = 𝑟𝑟𝑖𝑞𝑟 +𝑑

𝑑𝑡𝜓𝑞𝑟 + (𝜔𝑠 − 𝜔𝑟)𝜓𝑑𝑟 (3.4)

21

𝜓𝑑𝑠 = 𝐿𝑠𝑖𝑑𝑠 + 𝐿𝑚𝑖𝑑𝑟 (3.5)

𝜓𝑞𝑠 = 𝐿𝑠𝑖𝑞𝑠 + 𝐿𝑚𝑖𝑞𝑟 (3.6)

𝜓𝑑𝑟 = 𝐿𝑟𝑖𝑑𝑟 + 𝐿𝑚𝑖𝑑𝑠 (3.7)

𝜓𝑞𝑟 = 𝐿𝑟𝑖𝑞𝑟 + 𝐿𝑚𝑖𝑞𝑠 (3.8)

Here all the rotor quantities are referred to the stator. Now for stator flux oriented reference frame

it is certain that the quadrature axis flux is zero and the total flux is taken along the direct axis. i.e.

𝜓𝑞𝑠 =𝑑

𝑑𝑡𝜓𝑞𝑠 = 0 ; 𝜓𝑑𝑠 = 𝜓𝑠 (3.9)

i.e. 𝑖𝑑𝑠 =𝜓𝑠

𝑙𝑠−

𝑙𝑚

𝑙𝑠𝑖𝑑𝑟 ; 𝑖𝑞𝑠 = −

𝑙𝑚

𝑙𝑠𝑖𝑞𝑟 (3.10)

Substituting the above relations in voltage and flux linkage equations (3.1)-(3.8) the following

expressions are resulted which denotes the machine model in stator flux oriented reference frame

[18].

• 𝑣𝑑𝑠 =𝜓𝑠

𝜏𝑠−

𝑙𝑚

𝜏𝑠𝑖𝑑𝑟 +

𝑑

𝑑𝑡𝜓𝑠 (3.11)

• 𝑣𝑞𝑠 = 𝜔𝑠𝜓𝑠 −𝑙𝑚

𝜏𝑠𝑖𝑞𝑟 (3.12)

• 𝑣𝑑𝑟 = 𝑙𝑑

𝑑𝑡𝑖𝑑𝑟 − 𝑙(𝜔𝑠 − 𝜔𝑟)𝑖𝑞𝑟 + 𝑟𝑟𝑖𝑑𝑟 (3.13)

• 𝑣𝑞𝑟 = 𝑙𝑑

𝑑𝑡𝑖𝑞𝑟 + 𝑙(𝜔𝑠 − 𝜔𝑟)𝑖𝑑𝑟 + (𝑟𝑟𝑖𝑞𝑟 + (𝜔𝑠 − 𝜔𝑟)

𝑙𝑚

𝑙𝑠𝜓𝑠) (3.14)

Where l=𝑙𝑠𝑙𝑟−𝑙𝑚

2

𝑙𝑠 and τ𝑠 =

𝑙𝑠

𝑟𝑠

From the above equations one can see that when the magnitude of stator flux and rotational

frequency of the reference frame are maintained constant, the magnitude of stator voltage depends

22

only on the resistive drops which are negligible. Hence for maintaining constant voltage profile at

stator terminals there is a necessity to control the magnitude of stator flux vector along with its

rotational speed.

3.3 STATOR SIDE CONVERTER CONTROL

The block diagram of entire stator side converter control scheme is shown in Fig. 3.2.

Fig. 3.2 Schematic of stator side converter control scheme

As mentioned in the introduction, stator side converter is voltage controlled where the quadrature

axis and direct axis voltage components are generated as shown in the Fig. 3.2. The initial

conditions and final conditions of dc link voltage build up process are mentioned as follows:

𝜔𝑟 = 𝜔𝑟𝑠 > 0 , 𝜔𝑠 = 0, 𝜓𝑠 = 0, 𝑣𝑑𝑐 = 𝑉𝑑𝑜 > 0

𝜔𝑟 = 𝜔𝑟𝑠 , 𝜔𝑠 = 𝜔𝑠∗, 𝜓𝑠 = 𝜓, 𝑣𝑑𝑐 = 𝑉𝑑𝑐

23

The stator reference flux and actual flux are related by the following equation

𝜓𝑠 = 𝜓(1 − 𝑒−

𝑡

𝑡𝑠) (3.15)

From the stator voltage equations (3.9), (3.10) and the above target conditions we get the stator

voltage control variables as shown below [18].

𝑣𝑑𝑠∗ =

𝜓

𝑡𝑠−

𝑙𝑚

𝑡𝑠𝑖𝑑𝑟′𝑒 𝑎𝑛𝑑 𝑣𝑞𝑠

∗ = 𝜔𝑠∗𝜓𝑠 −

𝑙𝑚

𝑡𝑠𝑖𝑞𝑟′𝑒 (3.16)

Two stator phase voltages and two stator phase currents are sensed which are converted in to

stationary α-β components which are in turn used for the stator flux calculation and the unit vector

generation as shown below.

𝑣𝛼𝑠 = 𝑟𝑠𝑖𝛼𝑠 +𝑑

𝑑𝑡𝜓𝛼𝑠 ; 𝑣𝑞𝑠 = 𝑟𝑠𝑖𝑞𝑠 +

𝑑

𝑑𝑡𝜓𝑞𝑠 (3.17)

𝜓𝑠 = √(𝜓𝛼𝑠)2 + (𝜓𝛽𝑠)2 (3.18)

cos 𝜃𝑠 =𝜓𝛼𝑠

𝜓𝑠 ; sin 𝜃𝑠 =

𝜓𝛽𝑠

𝜓𝑠 (3.19)

The rotor three phase currents are sensed and they are converted in to d-q component currents in

reference frame which is oriented along the stator flux linkage vector, that are used for adding

compensating currents as shown in Fig. 3.2. Finally the reference voltages generated in d-q

reference frame are converted in to ABC reference frame using the unit vectors generated shown

in equation (3.19) and from these voltages the modulating signals are deduced for sine PWM

converter following the relation between the dc link voltage, fundamental component of output

voltage, and the modulation index as explained in the following section.

24

3.4 SPWM TECHNIQUE

Sine PWM technique is employed here because of its simplicity and also it is easy to implement a

sine triangular PWM technique compared to the Space Vector Pulse Width Modulation (SVPWM)

technique. Also in terms of performance sine PWM technique is almost similar to that of a space

vector PWM technique.

Fig. 3.3 Modulation signal of SPWM technique

For sine PWM inverter with Vd as dc input voltage and Vao as the fundamental component of ac

output voltage and mi as modulating index that is defined as ratio of the magnitude of modulating

signal to that of triangular carrier signal, the Fourier analysis of the output voltage gives the

following relation.

Vao=0.5miVd (3.20)

Where 𝑚𝑖 =𝑣𝑚𝑎

𝑣𝑇 (3.21)

Therefore expression for modulating signal can be deduced as follows

𝑣𝑚𝑎 =2𝑣𝑇

𝑣𝑑 (3.22)

25

This modulating signal is compared with triangular carrier wave of magnitude 𝑣𝑇 as shown in Fig.

3.3 for generation of pulses which are fed to the switches of the stator side converter.

3.5 ROTOR SIDE CONVERTER CONTROL

As it is already mentioned the rotor side converter is current controlled where the q-axis component

is used to nullify the power imbalance of the system through the dc link voltage controller which

modifies the quadrature current component according to the changes in the dc link voltage. The

schematic of the entire rotor converter control algorithm is shown in Fig. 3.4. Using the unit vectors

generated as shown in equation (3.19) for reference frame transformation the rotor currents and

stator currents are transformed in to their corresponding d-q axes components. The rotor flux

calculation is done using the rotor flux linkage equations (3.7) and (3.8) as mentioned in the

dynamic machine model. During the rise of dc link voltage at the capacitor terminals from a low

initial value to the desired level, the rotor currents are generated following the relations shown in

equation (3.23). During VSCF generation a dc link voltage controller comes in to picture which is

used to generate the q-axis rotor current and the d-axis rotor current is left undisturbed during

variable speed constant frequency generation. The difference between the actual dc link capacitor

voltage sensed and the reference voltage is fed to the PI controller as shown in Fig. 3.4. Initially

during the establishment of dc link voltage the rotor d-q current components are chosen as follows

[18].

𝑖𝑑𝑟∗ = 𝐼𝑑𝑟

∗ (1 − 𝑒−

𝑡

𝑇𝑑) ; 𝑖𝑞𝑟∗ = 𝐼𝑞𝑟

∗ (1 − 𝑒−

𝑡

𝑇𝑞) (3.23)

With the choice of these currents the dc link voltage gradually starts rising to its final reference

value which is governed by equation (3.24).

26

𝐶

3

𝑑𝑣𝑑2

𝑑𝑡= −(𝑣𝑞𝑠

𝑒∗𝑖𝑞𝑖𝑒 + 𝑣𝑑𝑠

𝑒∗𝑖𝑑𝑖𝑒 + 𝑣𝑞𝑟

′𝑒 𝑖𝑞𝑟′𝑒∗ + 𝑣𝑑𝑟

′𝑒 𝑖𝑞𝑟′𝑒∗) (3.24)

Once the dc link voltage reaches its desired reference value the switch shown in Fig. 3.4 is used to

connect the dc link voltage controller for generation of quadrature axis rotor current reference

component. The rotor flux d-q components are calculated using the relations shown in equations

(3.7) and (3.8) in section 3.2. These rotor flux components are used for calculating the

compensating terms that are to be added for reference voltage generation as shown in the schematic

diagram in Fig. 3.4.

Fig. 3.4 Schematic of rotor side converter control scheme

The direct axis rotor reference current is left undisturbed in the VSCF generation mode. The

difference between the reference values and actual values of the rotor currents is fed to the PI

controllers for generation of the corresponding reference voltage components in d-q reference

27

frame. These voltages are converted in to ABC reference frame using the reference angle for

transformation as shown in Fig. 3.5. From these reference voltages in ABC reference frame the

modulating signals are deduced in similar manner as explained for stator side converter control.

Finally the modulating signals are compared with triangular carrier waves for generation of pulses

which are fed to the rotor converter switches. Once the system enters in to VSCF generation mode

then only the load at the output terminals should be connected so that the system works

satisfactorily.

The unit vectors generated for stator flux orientation which are governed by the equation (3.19)

are shown below in Fig. 3.5(a) and Fig. 3.5(b).

Fig. 3.5(a) Unit vector sin (θs)

Fig. 3.5(b) Unit vector cos (θs)

3.6 SIMULATION RESUTLS AND DISCUSSION

In the simulated model the machine is rated at 5.6 kW and a load of 2.5 kW is considered. The

simulated model is tested for load transients and speed changes and its transient performance is

analyzed. First balanced linear load is considered and then nonlinear loads are concerned in the

next step. An initial dc link capacitor voltage of 30 volts is applied. The load is applied at 0.5

28

seconds and the rotor speed is maintained constant at 110 rad/sec up to 0.7 seconds and from 0.7

to 0.9 seconds the rotor speed is dropped from 110 to 70 rad/sec and from 0.9 seconds it is again

maintained constant which is shown in Fig. 3.6.

Fig. 3.6 Rotor speed

The direct axis and quadrature axis rotor current components are shown in Fig. 3.7 from which it

is clear that the q-axis current is changed from nearly zero to 10 amp at 0.5 seconds due to load

transient and again changes from 10 to 15 amperes during speed change which clearly shows that

dc link voltage controller commands the q-axis reference current.

Fig. 3.7 Rotor current in synchronous frame.

The dc link voltage profile is shown below in Fig. 3.8 from which it is clear that at 0.5 seconds as

the load is suddenly applied there is power imbalance due to which there is a slight dip in dc link

voltage and then it regains to its reference value as q-axis rotor current is increased accordingly.

29

Also from 0.7 to 0.9 seconds as the rotor speed is reduced there is again a slight dip in dc link

voltage profile which again regains its reference value due to increase in q-axis rotor current.

Fig. 3.8 dc link voltage profile

The load current waveform and load voltage waveform during load transients are shown in Fig.

3.9 and Fig. 3.10 respectively along with the FFT analysis of the load voltage which is shown in

Fig. 3.11. It is clear from Fig. 3.10 that there is a slight reduction in magnitude of load voltage

after the application of load at 0.5 seconds.

Fig. 3.9 Load current

Fig. 3.10 Load voltage profile

Fig. 3.11 FFT analysis of load voltage

30

The stator flux wave form along with d-q axes reference voltages generated from the stator side

converter control scheme are show in Fig. 3.12 and Fig. 3.13. From the graph in Fig. 3.12 it is

clear that the actual flux is aligned whit the reference stator flux which is 0.574 Weber’s.

Fig. 3.12 Stator flux

Fig. 3.13 Stator voltage in synchronous frame

The stator current profile is shown in Fig. 3.14 and its FFT analysis is shown in Fig. 3.15.

Fig. 3.14 Stator current

Fig. 3.15 FFT analysis of stator current

31

The load voltage profile for application of nonlinear load is shown in Fig. 3.16. The load current

profile and FFT analysis of load voltage are shown in Fig. 3.17 and Fig. 3.18 respectively for the

application of three phase nonlinear load which is a three phase diode rectifier circuit feeding an

R-L load.

Fig. 3.16 Load voltage for nonlinear load (open loop control)

Fig. 3.17 Load current for nonlinear load

Fig. 3.18 FFT analysis of load voltage for nonlinear load (open loop control)

From the load voltage waveform shown in Fig. 3.16 it is clear that there are unwanted distortions

in the load voltage with the application of nonlinear load.

Thus the open loop control strategy implemented in this model is not suitable for nonlinear loads

and unbalanced nonlinear loads as well.

32

Hence a closed loop control structure is implemented in the following chapter which works

satisfactorily for all loads (balanced, unbalanced, linear, nonlinear and unbalanced nonlinear).

33

CHAPTER 4

CLOSED LOOP CONTROL STRATEGY FOR DFIG BASED

STAND-ALONE WECS

4.1 INTRODUCTION

The schematic of the DFIG based stand-alone WECS with closed loop control strategy is shown

in Fig. 4.1. It consists of a WRIM with two PWM converters connected in back to back

configuration and are coupled with a common dc link capacitor. The rotor of the machine is

connected to a prime mover. The two converters are named as stator converter and rotor converter

respectively. Ac side of the stator converter is connected to the machine stator terminals via an

inductive filter as show in Fig. 4.1. A capacitive filter is connected at the junction to which load

terminals are connected through a switch. The only difference between the configurations adopted

for open loop scheme and that of closed loop scheme is that of the placement of inductive filter.

In the present configuration as the inductive filter is placed in between the machine stator terminals

and stator converter terminals it is expected to give good voltage regulation at the output terminals

as the load is connected to the stator terminals at the capacitor filter junction without any inductive

filter between the load and stator terminals. The control algorithm used for this configuration is

same as that of open loop control structure except an additional stator voltage control strategy is

implemented in the stator side converter control. The stator converter is voltage controlled

converter where the difference between the reference voltage and actual voltage is fed to stator

voltage controller that accordingly modifies the reference inverter output voltages.

34

Fig. 4.1 Schematic of DFIG based stand-alone system with closed loop control scheme

The rotor converter is current controlled where the quadrature axis rotor reference current is

generated using a dc link voltage controller so that it maintains the power balance of the system.

Whenever there is any power imbalance in the system the corresponding change will be reflected

in the dc link capacitor voltage. For example when there is sudden increase in the load there will

be a fall in the dc link voltage and accordingly the quadrature axis rotor current is forced to increase

so that torque will increase which increases the total output power and nullifies the power

imbalance in the entire system. In this manner whenever there are load changes and speed changes,

the q-axis rotor current will be adjusted accordingly so that power balance is maintained. The entire

rotor side converter control is similar to that explained in third chapter for open loop control

strategy and its block diagram is shown in Fig. 3.4. Hence in the current chapter a major focus will

be given on stator voltage controller as follows.

35

4.2 STATOR SIDE CONVERTER CONTROL

The stator reference voltages are generated according to the equation (3.16) given in chapter 3 and

the entire schematic of stator side converter is also shown in Fig. 3.2 in chapter 3. Now in this

closed loop control scheme the capacitor filter is forced to maintain these reference voltages

generated and this process is achieved by means of a stator voltage controller. Before having a

deep insight in to this stator voltage controller there is a need to represent the stator side inverter

along with inductive filter in dq synchronous reference frame and is shown below. The direct axis

and quadrature axis equivalent circuits of stator side inverter along with filter are shown in Fig.

4.2 and Fig. 4.3 respectively.

Fig. 4.2 equivalent circuit in d-axis.

Fig. 4.3 equivalent circuit in q-axis

36

The voltage and current equations governing the d-q axes equivalent circuits expressed in

synchronous reference frame are as follows [18]:

𝑐𝑓𝑑

𝑑𝑡𝑣𝑑𝑐 = 𝑖𝑑𝑓 − 𝑖𝑑𝑙 − 𝑖𝑑𝑠 + 𝜔𝑠𝑐𝑓𝑣𝑞𝑐 (4.1)

𝑐𝑓𝑑

𝑑𝑡𝑣𝑞𝑐 = 𝑖𝑞𝑓 − 𝑖𝑞𝑙 − 𝑖𝑞𝑠 − 𝜔𝑠𝑐𝑓𝑣𝑑𝑐 (4.2)

𝑣𝑑𝑖 = 𝑟𝑓𝑖𝑑𝑓 + 𝑙𝑓𝑑

𝑑𝑡𝑖𝑑𝑓 − 𝜔𝑠𝑙𝑓𝑖𝑞𝑓 + 𝑣𝑑𝑐 (4.3)

𝑣𝑞𝑖 = 𝑟𝑓𝑖𝑞𝑓 + 𝑙𝑓𝑑

𝑑𝑡𝑖𝑞𝑓 + 𝜔𝑠𝑙𝑓𝑖𝑑𝑓 + 𝑣𝑞𝑐 (4.4)

As the capacitor terminals are directly connected to the machine stator terminals the voltage at the

capacitor terminals is same as that of the stator voltage and hence it can be written as follows.

𝑣𝑑𝑐 = 𝑣𝑑𝑠 𝑎𝑛𝑑 𝑣𝑞𝑐 = 𝑣𝑞𝑠 (4.5)

The schematic of stator voltage controller is shown in Fig. 4.4. The two phase quantities of stator

voltage, stator current, filter current, and load current are sensed and are transformed in to their

corresponding d-q quantities in synchronously rotating reference frame using the unit vector

signals shown in equation (3.19) for transformation. All these quantities are fed to the stator

voltage controller along with the stator d-q axes reference voltages whose generation is already

explained in the previous chapter. The stator voltage controller generates the reference voltage

signals for stator side inverter in synchronous reference frame after adding the compensating terms

which are as shown in the schematic diagram of stator voltage controller in Fig. 4.4.

37

Fig. 4.4 Schematic of stator voltage controller [18].

The reference voltages for stator side inverter in synchronously rotating reference frame are then

transformed in to three phase quantities expressed in ABC reference frame. These reference signals

generated are processed to get the modulation signals for sine PWM technique which are compared

with triangular carrier waves for generation of pulses. These pulses are then fed to the switches of

the stator side converter.

4.3 SIMULATION RESULTS AND DISCUSSION

In the simulated model the machine is rated at 5.6 kW and a load of 2.5 kW is considered. The

simulated model is tested for load transients and speed changes and its transient performance is

analyzed. First balanced linear load is considered and then nonlinear loads are concerned in the

next step. An initial dc link capacitor voltage of 30 volts is applied. The load is applied at 0.5

seconds and the rotor speed is maintained constant at 110 rad/sec up to 0.7 seconds and from 0.7

𝜔𝑠𝑐𝑓𝑣𝑑𝑠

𝜔𝑠𝑐𝑓𝑣𝑞𝑠

38

to 0.9 seconds the rotor speed is dropped from 110 to 70 rad/sec and from 0.9 seconds it is again

maintained constant as already shown in Fig. 3.6.

The dc link voltage profile is shown in Fig. 4.5 having a transient at 0.5 sec due to sudden

application of load and the rotor current in synchronous reference frame is shown in Fig. 4.6 where

the q-axis rotor current rises at 0.5sec due to load change and also from 0.7 to 0.9 sec it increases

linearly to compensate fall in speed accordingly.

Fig. 4.5 dc link voltage profile

Fig. 4.6 Rotor current in synchronous reference frame

The stator flux and stator voltage in synchronous reference frame are shown in Fig. 4.7 and Fig.

4.8 where the actual values are forced to align with the reference values by the controller action.

Fig. 4.7 Stator flux

39

Fig. 4.8 Stator voltage in synchronous reference frame

The stator current, load current and load voltage profiles are shown in Fig. 4.9, Fig. 4.10 and Fig.

4.11 respectively. From the load voltage profile it is clear that there is negligible voltage drop at

the load terminals during sudden application of the load at 0.5 sec which shows that this model

exhibits good load voltage regulation compared to the one with open loop control scheme.

Fig. 4.9 Stator current

Fig. 4.10 Load current

Fig. 4.11 Load voltage

40

Now the model is tested for a balanced nonlinear load which is nothing but a three phase diode

rectifier supplying an R-L load. The load current is shown in Fig. 4.13. The stator current along

with its FFT analysis is shown in Fig. 4.14 and in Fig. 4.15 respectively.

Fig. 4.12 Load current for nonlinear load

Fig. 4.13 Stator current

Fig.4.14 FFT analysis of stator current

Fig. 4.15 Load voltage profile for nonlinear load (closed loop control)

41

Fig. 4.16 FFT analysis of load voltage for nonlinear load (closed loop control)

The load voltage profile and its FFT analysis during load transient is shown in Fig. 4.16 and Fig.

4.17 respectively. From the load voltage profile shown in Fig. 4.16 it is clear that this model works

satisfactorily for nonlinear loads and also there are no unwanted distortions in the load voltage

unlike that of the model with open loop control scheme as explained in the previous chapter.

42

CHAPTER 5

CONCLUSIONS AND FUTURE SCOPE

The wound rotor induction machine dynamic models in different reference frames are studied and

analyzed as a clear understanding is required for developing control algorithms for DFIG based

stand-alone WECS. Two control algorithms are developed for two different configurations for

achieving the desired objectives. One is open loop control scheme and the other is closed loop

control structure. In the open loop control scheme a constant voltage magnitude and constant

frequency is maintained at the output terminals and its transient performance is analyzed during

sudden load transients and prime mover speed changes. But with this open loop scheme the

following problems are encountered which enhances the need for closed loop control strategy.

Poor load voltage regulation at the output terminals.

Unwanted distortions are coming in to picture in load voltage profile for the application of

nonlinear loads. Therefor this scheme is suitable only for balanced linear loads and it

cannot be used for other categories of load.

In the closed loop control scheme a slight modification is done in the configuration and a direct

stator voltage controller is added in the stator side converter control and this scheme is able to

maintain all the desired qualities which are mentioned below.

Maintaining constant magnitude and constant frequency voltage profile at the output

terminals against the load transients and prime mover speed changes.

Good load voltage regulation at the output terminals.

43

Satisfactory operation for all types of loads which may be linear, nonlinear and unbalanced

nonlinear loads as well.

FUTURE SCOPE

Some interesting areas for further studies are as follows.

Hardware implementation of the model with closed loop control strategy using Field-

Programmable Gate Array (FPGA).

Modelling of DFIG based stand-alone WECS along with battery storage.

Application of matrix converters in DFIG based wind energy conversion system as they

are capable of ac to ac conversion.

Study of grid connected operation of DFIG based WECS.

44

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